Antiferromagnetic quantum spins on the pyrochlore lattice

The ground state of the S = 1/2 Heisenberg antiferromagnet on the pyrochlore lattice is theoretically investigated. Starting from the limit of isolated tetrahedra, I include interactions between the tetrahedra and obtain an effective model for the spin-singlet ground state multiplet by third-order perturbation. I determine its ground state using the mean-field approximation and find a dimerized state with a four-sublattice structure, which agrees with the proposal by Harris et al. I also discuss chirality correlations and spin correlations for this state.